The LATTICE Procedure

Example 50.1 Analysis of Variance through PROC LATTICE

In the following example, from Cochran and Cox (1957, p. 406), the data are yields (`Yield`) in bushels per acre of 25 varieties (`Treatment`) of soybeans. The data are collected in two replications (`Group`) of 25 varieties in five blocks (`Block`) containing five varieties each. This is an example of a partially balanced square lattice design.

```data Soy(drop=plot);
do Group = 1 to 2;
do Block = 1 to 5;
do Plot = 1 to 5;
input Treatment Yield @@;
output;
end;
end;
end;
datalines;
1  6  2  7  3  5  4  8  5  6  6 16  7 12  8 12  9 13 10  8
11 17 12  7 13  7 14  9 15 14 16 18 17 16 18 13 19 13 20 14
21 14 22 15 23 11 24 14 25 14  1 24  6 13 11 24 16 11 21  8
2 21  7 11 12 14 17 11 22 23  3 16  8  4 13 12 18 12 23 12
4 17  9 10 14 30 19  9 24 23  5 15 10 15 15 22 20 16 25 19
;
```
```proc print data=Soy;
id Treatment;
run;
```
```proc lattice data=Soy;
run;
```

The results from these statements are shown in Output 50.1.1 and Output 50.1.2.

Output 50.1.1: Displayed Output from PROC PRINT

Treatment Group Block Yield
1 1 1 6
2 1 1 7
3 1 1 5
4 1 1 8
5 1 1 6
6 1 2 16
7 1 2 12
8 1 2 12
9 1 2 13
10 1 2 8
11 1 3 17
12 1 3 7
13 1 3 7
14 1 3 9
15 1 3 14
16 1 4 18
17 1 4 16
18 1 4 13
19 1 4 13
20 1 4 14
21 1 5 14
22 1 5 15
23 1 5 11
24 1 5 14
25 1 5 14
1 2 1 24
6 2 1 13
11 2 1 24
16 2 1 11
21 2 1 8
2 2 2 21
7 2 2 11
12 2 2 14
17 2 2 11
22 2 2 23
3 2 3 16
8 2 3 4
13 2 3 12
18 2 3 12
23 2 3 12
4 2 4 17
9 2 4 10
14 2 4 30
19 2 4 9
24 2 4 23
5 2 5 15
10 2 5 15
15 2 5 22
20 2 5 16
25 2 5 19

Output 50.1.2: Displayed Output from PROC LATTICE

The Lattice Procedure

Analysis of Variance for Yield
Source DF Sum of Squares Mean Square
Replications 1 212.18 212.18
Blocks within Replications (Adj.) 8 501.84 62.7300
Component B 8 501.84 62.7300
Intra Block Error 16 218.48 13.6550
Randomized Complete Block Error 24 720.32 30.0133
Total 49 1491.78 30.4445

Variance of Means in Same Block 15.7915
Variance of Means in Different Bloc 17.9280
Average of Variance 17.2159
LSD at .01 Level 12.1189
LSD at .05 Level 8.7959
Efficiency Relative to RCBD 174.34

Means for Yield
Treatment Mean
1 19.0681
2 16.9728
3 14.6463
4 14.7687
5 12.8470
6 13.1701
7 9.0748
8 6.7483
9 8.3707
10 8.4489
11 23.5511
12 12.4558
13 12.6293
14 20.7517
15 19.3299
16 12.6224
17 10.5272
18 10.7007
19 7.3231
20 11.4013
21 11.6259
22 18.5306
23 12.2041
24 17.3265
25 15.4048

The efficiency of the experiment relative to a randomized complete block design is 174.34%. Precision is gained using the lattice design via the recovery of intra-block error information, enabling more accurate estimates of the treatment effects. Variety 8 of soybean had the lowest adjusted treatment mean (6.7483 bushels per acre), while variety 11 of soybean had the highest adjusted treatment mean (23.5511 bushels per acre).